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Theorem rexv 2730
Description: An existential quantifier restricted to the universe is unrestricted. (Contributed by NM, 26-Mar-2004.)
Assertion
Ref Expression
rexv  |-  ( E. x  e.  _V  ph  <->  E. x ph )

Proof of Theorem rexv
StepHypRef Expression
1 df-rex 2441 . 2  |-  ( E. x  e.  _V  ph  <->  E. x ( x  e. 
_V  /\  ph ) )
2 vex 2715 . . . 4  |-  x  e. 
_V
32biantrur 301 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43exbii 1585 . 2  |-  ( E. x ph  <->  E. x
( x  e.  _V  /\ 
ph ) )
51, 4bitr4i 186 1  |-  ( E. x  e.  _V  ph  <->  E. x ph )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104   E.wex 1472    e. wcel 2128   E.wrex 2436   _Vcvv 2712
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-rex 2441  df-v 2714
This theorem is referenced by:  rexcom4  2735  spesbc  3022  abnex  4407  dfco2  5085  dfco2a  5086
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